The lollipop graph is determined by its Q-spectrum

A graph GG is said to be determined by its Q-spectrum   if with respect to the signless Laplacian matrix QQ, any graph having the same spectrum as GG is isomorphic to GG. The lollipop graph  , denoted by Hn,pHn,p, is obtained by appending a cycle CpCp to a pendant vertex of a path Pn−pPn−p. In this paper, it is proved that all lollipop graphs are determined by their QQ-spectra.